Blend the strawberries, lime juice, and honey in a high-speed blender. (You will want to drink this with a straw, but try to refrain.)
Rub the rims of two glasses with a slice of lime then dip in a shallow bowl of sugar. Add ice to glasses.
In a cocktail shaker, muddle 6-10 mint leaves with a muddler or the back of a wooden spoon. Then add 1 1/2 cups ice, gin and 1/2 - 3/4 cup strawberry puree mixture. Shake well.
If you prefer no seeds, you can strain this through a fine mesh sieve. I did not.
Pour mixture into glasses and top with club soda.
Garnish with fresh lime, strawberries, and mint.
Serve with a straw. You may have some leftover strawberry puree - pour it on top of vanilla ice cream.